I. Field of the Invention
This invention relates generally to the slicing of a three-dimensional object representation into layer representations for subsequent use in the stepwise layer-by-layer formation of the three-dimensional object through application of the principles of stereolithography, and more specifically, to the slicing of the object representation into the layer representations utilizing boolean comparisons between the borders of successive layers.
II. Background of the Invention
Several building techniques have recently become available for building three-dimensional objects in layers. One such technique is stereolithography, which is described in U.S. Pat. Nos. 4,575,330 and 4,929,402 (hereinafter the '330 and the '402 patents), the disclosures of which are hereby fully incorporated by reference herein as though set forth in full. According to the principles of stereolithography, a three-dimensional object is formed layer-by-layer in a stepwise fashion out of a material capable of physical transformation upon exposure to synergistic stimulation. In one embodiment of stereolithography, layers of untransformed material such as liquid photopolymer or the like are successively formed at the working surface of a volume of the liquid photopolymer contained in a container. The untransformed layers are successively formed over untransformed material and previously-transformed material. The process of forming these untransformed layers is known as a recoating step, and is described in detail in Ser. No. 515,479, now U.S. Pat. No. 5,174,931.
These layers are then selectively exposed to the synergistic stimulation to form successive object cross-sections. Moreover, upon transformation into the object cross-sections, the transformed material typically adheres to the previously-formed cross-sections through the natural adhesive properties of the photopolymer upon solidification. Additional details about stereolithography are available in the following co-pending U.S. patent applications, all of which, including appendices, are hereby fully incorporated by reference herein as though set forth in full:
______________________________________ Application Ser. No. Filing Date Inventor(s) Status ______________________________________ 07/182,830 Apr. 18, 1988 Hull et al. U.S. Pat. No. 5,059,359 07/183,016 Apr. 18, 1988 Modrek U.S. Pat. No. 4,996,010 07/182,801 Apr. 18, 1988 Hull, et al. U.S. Pat. No. 4,999,143 07/183,015 Apr. 18, 1988 Smalley U.S. Pat. No. 5,015,424 07/268,429 Nov. 8, 1988 Modrek U.S. Pat. No. 5,076,974 et al. 07/268,816 Nov. 8, 1988 Spence U.S. Pat. No. 5,058,988 07/268,837 Nov. 8, 1988 Spence U.S. Pat. No. 5,123,734 et al. 07/268,907 Nov. 8, 1988 Spence U.S. Pat. No. 5,059,021 et al. 07/331,644 Mar. 31, 1989 Hull et al. U.S. Pat. No. 5,184,307 07/339,246 Apr. 7, 1989 Hull et al. U.S. Pat. No. 5,104,592 07/365,444 Jun. 12, 1989 Leyden U.S. Pat. No. 5,143,663 et al. 07/414,200 Oct. 27, 1989 Hull et al. Abandoned 07/415,168 Sept. 29, 1989 Hull et al. Abandoned 07/429,911 Oct. 27, 1989 Spence U.S. Pat. No. 5,182,056 et al. 07/427,885 Oct. 27, 1989 Spence U.S. Pat. No. 5,133,987 et al. 07/428,492 Oct. 27, 1989 Vorgitch Abandoned et al. 07/429,435 Oct. 30, 1989 Smalley U.S. Pat. No. 5,130,064 et al. 07/495,791 Mar. 19, 1990 Jacobs Abandoned et al. 07/515,479 Apr. 27, 1990 Almquist U.S. Pat. No. 5,174,931 et al. 07/545,517 Jun. 28, 1990 Cohen U.S. Pat. No. 5,096,530 07/566,527 Aug. 13, 1990 Jacobs Abandoned et al. ______________________________________
Additional details of stereolithography are also available in two related applications which are being filed concurrently herewith. The disclosures of these two additional applications are hereby fully incorporated by reference herein as though set forth in full.
The first of these concurrently-filed applications is U.S. patent application Ser. No. 07/606,802, now U.S. Pat. No. 5,192,469 entitled "Simultaneous Multiple Layer Curing for Forming Three-Dimensional Objects," filed by Smalley et al. This application describes methods of building high resolution objects from traditionally low-resolution combinations of building materials and synergistic stimulation, which combinations result in a minimum effective cure depth which is typically too deep to form the thin layers required for high resolution objects. This objective is accomplished by delaying the exposure of those areas on a particular cross-section that would negatively impact resolution if those areas were immediately cured upon formation of the cross-section. Resolution may be negatively impacted, for example, if, because of the cure depth involved, material below this cross-section is inadvertently cured upon exposure of these areas. Therefore, to preserve resolution, exposure of these areas is delayed, and corresponding areas which are above these areas on higher cross-sections are instead subsequently exposed, after a delay if necessary, which higher cross-sections are chosen such that the cure depth is deep enough to cure the desired areas without inadvertently curing material on lower cross-sections.
The second of these concurrently-filed applications is U.S. patent application Ser. No. 07/605,979, now U.S. Pat. No. 5,209,878 entitled "Improved Surface Resolution in Three-Dimensional Objects by Inclusion of Thin Fill Layers," filed by Smalley et al. This application describes methods for forming high resolution objects by filling the surface discontinuities inherent in three-dimensional objects formed from stereolithography with thin fill layers.
Other embodiments of stereolithography employ materials besides photopolymers such as powdered materials, thermoplastics, dry film photoresists, non-reactive pre-formed films or sheets, all of which share the common characteristics that they are capable of physical transformation upon exposure to an appropriate form of synergistic stimulation. Moreover, a variety of types of synergistic stimulation are possible, other than UV radiation from a laser, including infrared or CO.sub.2 laser radiation, visible radiation, particle beam radiation, reactive chemical agents dispensed from ink jet type printing heads (e.g., binders and initiators) and the like. In addition, various means for selectively exposing the untransformed layers of material are possible, including rotatable scanning mirrors or the like for directing a beam of the synergistic stimulation to trace out the shape of the object layers on the untransformed layers, means such as a mask for selectively applying flood exposure to the untransformed layers, means such as a light valve, imaging system or the like, and xy tables for translating a dispenser for chemical synergistic stimulation or the like.
Various means of performing the recoating process are possible. The '330 patent describes the use of a platform coupled to a Z-stage elevator to overdip a previously-formed layer beyond the working surface as an expeditious means to perform recoating. U.S. patent application Ser. No. 07/515,479 describes the use of a doctor blade to speed up the recoating process. U.S. patent application Ser. No. 07/495,791 describes the use of vibrational forces to speed up the recoating process. Additional approaches, which are possible, include dispensing pre-formed sheets or films over a previously-formed layer from a roll or cartridge dispenser. Also, various means of moving the partially-formed part relative to the working surface, besides a platform coupled to a Z-stage elevator, are possible, including means for adding or extracting material from the container, or means for moving the container relative to the partially-formed part. Also, various other means of adhering the layers together, besides the natural adhesive properties of the material being used, are also possible, including pressure or heat sensitive adhesives or the like.
As can be seen from the above description, a wide variety of embodiments are included within the term "stereolithography," all having the common characteristic of being capable of forming a three-dimensional object in a step-wise layer-by-layer fashion.
As described in Ser. No. 331,644, a stereolithography system will typically form a three-dimensional object in accordance with a corresponding object representation, which representation may be formed in a CAD system or the like. Before such a representation can be used, however, as described in Ser. No. 331,644, it must be sliced into a plurality of layer representations. The stereolithography system will then, in the course of building up the object in a stepwise layer-by-layer manner, selectively expose the untransformed layers of material in accordance with the layer representations to form the object layers, and thus, the object itself.
Previous methods of forming the layer representations suffered from a number of disadvantages, however.
First, these methods typically do not make direct use of an object representation generated from a CAD system. Instead, these methods typically require that the object representation be placed into an intermediate format, i.e., a tesselated triangle format, before being useful to the stereolithography system. Because of this limitation, these methods do not have wide applicability, and can only be used with those CAD systems which have the capability of formatting the object representation appropriately. As a result, they are not presently capable of directly utilizing object representations such as CAT scans or the like, which may originate from systems presently incapable of formatting the object representations into the required format.
A second problem with these methods is that they typically assume, in furtherance of achieving computational simplicity, that all portions of a layer will overlap, and therefore, adhere to a previous layer. Therefore, because it is advantageous to slightly overcure these overlapping areas by about 6 mils beyond the specified layer thickness, these methods will overcure all portions of a layer, even those portions that do not overlap previous layers, such as down-facing regions. The result is that part accuracy, and part aesthetics, are negatively impacted, especially at the down-facing regions.
A third problem with these methods is that they are typically inflexible, being capable of specifying either an oversized object or an undersized object, but not both..sup.1/ However, for certain objects, only one of these techniques will be possible. For example, for a complex object, it may be impossible to sand certain, inaccessible areas, so that the undersized technique is the only reasonable one. Therefore, for these objects, past methods have not provided necessary flexibility. FNT .sup.1/ As explained in Ser. No. 331,644, building an oversized or an undersized object enables the surface discontinuities inherent to stereolithography to be smoothed out in a subsequent post-processing step.
A fourth problem with these methods is that they sometimes introduce a vertical registration problem into a part. As explained in Ser. No. 331,644, in furtherance of the interest of computational simplicity, these methods generally create the borders of each layer representation at a vertical position slightly offset from the rest of the layer representation..sup.2/ By doing so, each object layer, once built, will be offset one layer thickness downwards from the corresponding object representation. That is, it will not be correctly vertically registered with the part. Normally, this misregistration will not be a problem if the layer thickness for all object layers is the same, since all object layers will be shifted downwards by the same amount. However, if two object representations are sliced with two different layer thicknesses and then merged and built simultaneously, then each individual object will be vertically shifted downwards by a different amount causing these individual objects to become incorrectly vertically registered relative to each other. FNT .sup.2/ This ensures that the correct number of layer representations are formed. If the borders were to be created at the same vertical level as the rest of the layer, then one too many layer representations would generally be formed.
This problem can be explained more fully with the aid of FIGS. 1a-1b. FIG. 1a shows object representation 1a, and leg representations 1b and 1c. It is assumed that the object representation will be sliced at a smaller layer thickness than the layer thickness used to slice the legs.
FIG. 1a also shows the object and leg representations being sliced by slicing layers 2a-2g into object layer representations 3a-3f. The number of object layer representations is (correctly) one less than the number of slicing layers.
As mentioned earlier, the object layers formed from each layer representation will be displaced one layer thickness downwards from the corresponding layer representation. FIG. 1b shows object (and leg) layers 3a'-3f', each of which is offset one layer thickness downwards from the corresponding layer representations 3a-3f shown in FIG. 1a.
As indicated, layers 3e' and 3f' have been moved downwards farther than layers 3a'-3d', with the result that these layers are no longer in physical contact with each other. This exemplifies the vertical misregistration problem referred to above.
A fifth problem With these methods is that they do not always generate near-flat skins (described in Ser. No. 331,644) in those instances where they would improve surface resolution. Instead, these methods typically only generate near-flat skins to avoid material leakage, with the result that these methods sometimes avoid creating near-flat skins which could contribute to part accuracy.
This problem can be illustrated with the aid of FIG. 2, which shows an envelope 4 of an object representation, cross-sectional outline 5a of a first object layer, and cross-sectional outline 5b of a second underlying object layer.
As indicated, there is a gap 8 between the layers which could allow leakage of untransformed material unless the gap were to be plugged with near-flat skin.
The decision whether to generate near-flat skin will be based on a comparison between normal 6, the vertical axis 7, the angle between the normal 6 and the vertical axis 7, and the minimum surface angle ("MSA")..sup.3/ If this angle is less than the minimum surface angle, then near-flat skins will be generated to close the gap. FNT .sup.3/ The MSA is the minimum angle between normal 6 and the vertical 7 which will guarantee that the cross-sections 5a and 5b will touch, closing gap 8, and preventing material from leaking out of the gap.
Therefore, in the usual case, near-flat skins will not be generated when the cross-sections 5a and 5b are touching, as shown in FIG. 3. However, even in this instance, the addition of near-flat skins would still provide a surface which more appropriately represents the object representation 4, thereby ensuring appropriate formation of an oversized or undersized object.
A sixth problem with these methods is that it is difficult to utilize techniques for achieving enhanced surface resolution, including simultaneous multiple layer transformation, as described in U.S. patent application Ser. No. 07/606,802, filed concurrently herewith, or generation of extra fill layers, as described in U.S. patent application Ser. No. 07/605,979, also filed concurrently herewith, with these methods. This is because the methods and techniques in these referenced applications inherently involve the comparison of cross-sectional information between two or more layers. Without a generalized layer comparison capability, the required comparisons (for the referenced applications) must be separately developed for each particular case and for each particular operation that will be performed.
A seventh problem with the vector-based implementations of these methods is that they typically overcure intersection points between border vectors describing the borders of the layers, and hatch or skin vectors describing the interior portions of the layers. Because of this overcuring, a significant distortion may be introduced at the intersection points, both because the cure depth of these points will be too deep, but also since the cure width, which increases proportionally to the cure depth, will also be too large.
Therefore, it is an object of the present invention to provide a slicing apparatus and method which is less dependent on a particular input format, and which is therefore compatible with a wider range of systems generating object representations, including CAT scan systems or the like, or CAD systems which do not necessarily provide the tesselated triangular format.
It is a further object to provide a slicing apparatus and method which distinguishes more fully between down-facing regions and the remaining areas encompassed by the layer borders, so that the overcure of the down-facing regions can be prevented.
It is a further object to provide a slicing apparatus and method which generates layer borders from portions of the object representation which are not vertically offset from those portions used to generate the interior portions of the layers.
A further object is to provide a slicing apparatus and method which is more flexible in switching between providing oversized, undersized, and average-sized parts, as well as other sizing schemes.
A further object is to provide a slicing apparatus and method which reduces or eliminates the vertical registration problem.
A further object is to provide a slicing apparatus and method which generally produces near-flat skins when they would improve the surface resolution of the object.
A further object is to provide a slicing apparatus and method which is more compatible with additional processes for improving surface resolution, including simultaneous multiple layer transformation, and the generation of thin fill layers.
A further object is to provide a slicing apparatus and method which retracts skin and/or hatch vectors from intersection points with border vectors, thereby reducing unintended overexposure of material at the intersection points.
Additional objects and advantages will be set forth in the description which follows or will be apparent to those of ordinary skill in the art who practice the invention.